Question

The instructions for a woodwork project call for three pieces of wood. The longest piece must be twice the length of the middle-sized piece, and the shortest must be 10 inches shorter than the middle-sized piece. Maria has a board 70 inches long that she wishes to use. How long can each piece be?

A) Longest: 40 inches, Middle-sized: 20 inches, Shortest: 10 inches
B) Longest: 50 inches, Middle-sized: 25 inches, Shortest: 15 inches
C) Longest: 60 inches, Middle-sized: 30 inches, Shortest: 20 inches
D) Longest: 70 inches, Middle-sized: 35 inches, Shortest: 25 inches

Answer 1

The correct option is: A) Longest: 40 inches, Middle-sized: 20 inches, Shortest: 10 inches

Let's represent the lengths of the three pieces as follows:

Longest piece: L

Middle-sized piece: M

Shortest piece: S

The problem states that the longest piece is twice the length of the middle-sized piece, which can be expressed as:

L = 2M

The shortest piece is 10 inches shorter than the middle-sized piece, which can be expressed as:

S = M - 10

We also know that the total length of the three pieces is 70 inches, which can be expressed as:

L + M + S = 70

(2M) + M + S = 70

Combine like terms:

3M + S = 70

Substitute the second equation (S = M - 10) into the above equation to get:

3M + (M - 10) = 70

4M - 10 = 70

Add 10 to both sides:

4M = 80

M = 20

L = 2(20) = 40

S = 20 - 10 = 10

Longest: 40 inches, Middle-sized: 20 inches, Shortest: 10 inches